

import math
import sys


def 					_UpperCAmelCase				(						a__):

			'''simple docstring'''



			if number != int(a__):
						raise ValueError("""the value of input must be a natural number""")
			if number < 0:
						raise ValueError("""the value of input must not be a negative number""")
			if number == 0:
						return 1
			a_						:						Dict 							= [-1] * (number + 1)
			a_						:						List[Any] 							= 0
			for i in range(1  ,	number + 1):
						a_						:						int 							= sys.maxsize
						a_						:						List[str] 							= int(math.sqrt(a__))
						for j in range(1  ,	root + 1):
									a_						:						Dict 							= 1 + answers[i - (j**2)]
									a_						:						Optional[Any] 							= min(a__  ,	a__)
						a_						:						Union[str, Any] 							= answer
			return answers[number]


if __name__ == "__main__":
	import doctest

	doctest.testmod()





from random import randint
from tempfile import TemporaryFile

import numpy as np


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__):

			'''simple docstring'''



			a_						:						List[Any] 							= 0
			if start < end:
						a_						:						Dict 							= randint(a__  ,	a__)
						a_						:						List[str] 							= a[end]
						a_						:						Tuple 							= a[pivot]
						a_						:						Tuple 							= temp

						a_							,					a_						:						List[Any] 							= _in_place_partition(a__  ,	a__  ,	a__)
						count += _in_place_quick_sort(a__  ,	a__  ,	p - 1)
						count += _in_place_quick_sort(a__  ,	p + 1  ,	a__)
			return count


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__):

			'''simple docstring'''



			a_						:						Optional[int] 							= 0
			a_						:						Union[str, Any] 							= randint(a__  ,	a__)
			a_						:						Union[str, Any] 							= a[end]
			a_						:						Any 							= a[pivot]
			a_						:						Any 							= temp
			a_						:						int 							= start - 1
			for index in range(a__  ,	a__):
						count += 1
						if a[index] < a[end]:  # check if current val is less than pivot value
									a_						:						str 							= new_pivot_index + 1
									a_						:						Optional[Any] 							= a[new_pivot_index]
									a_						:						str 							= a[index]
									a_						:						Union[str, Any] 							= temp

			a_						:						Union[str, Any] 							= a[new_pivot_index + 1]
			a_						:						Tuple 							= a[end]
			a_						:						Any 							= temp
			return new_pivot_index + 1, count


__snake_case				:      Union[str, Any]   		=			TemporaryFile()
__snake_case				:      Dict   		=			1_00  # 1000 elements are to be sorted


__snake_case		, __snake_case				:      int   		=			0, 1  # mean and standard deviation
__snake_case				:      Tuple   		=			np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("""The array is""")
print(X)


outfile.seek(0)  # using the same array
__snake_case				:      str   		=			np.load(outfile)
__snake_case				:      Dict   		=			len(M) - 1
__snake_case				:      Dict   		=			_in_place_quick_sort(M, 0, r)

print(
    """No of Comparisons for 100 elements selected from a standard normal distribution"""
    """is :"""
)



print(z)


